A250162 Number of length n+1 0..3 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

4, 20, 96, 436, 1880, 7836, 32032, 129572, 521256, 2091052, 8376368, 33529908, 134168632, 536772668, 2147287104, 8589541444, 34358952008, 137437380684, 549752668240, 2199016964180, 8796080439384, 35184346923100, 140737438023776

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..59

Formula

Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).

Conjectures from Colin Barker, Nov 12 2018: (Start)

G.f.: 4*x*(1 - 3*x + 5*x^2) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).

a(n) = 2*(2 - 3*2^n + 4^n + 2*n).

(End)

Example

Some solutions for n=6:
..1....3....3....2....3....2....2....2....2....1....1....2....1....0....2....1
..1....0....2....3....3....0....2....2....2....1....0....0....1....2....0....0
..0....3....1....3....3....2....3....3....2....3....3....0....1....2....3....2
..3....1....0....0....0....3....1....1....2....2....3....2....3....3....0....1
..0....2....3....3....3....2....3....2....1....0....1....3....3....1....2....2
..1....1....0....1....3....0....2....0....0....1....2....2....0....3....0....2
..3....3....1....2....3....2....2....0....2....3....1....0....1....2....2....3

Crossrefs

Column 3 of A250167.

Sequence in context: A254943 A099025 A008353 * A296665 A057087 A151254

Adjacent sequences: A250159 A250160 A250161 * A250163 A250164 A250165

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved